Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with coxeter-groups
Search options not deleted
user 4231
A Coxeter group is a group defined by a presentation by involutions $r_i$ with relators $(r_ir_j)^{m_{ij}}=1$ for certain family $(m_{ij})$ of integers greater than 1.
8
votes
Accepted
How to think about the simple reflection $s_0$ in the affine Weyl group?
You are asking several questions here, so it may be useful to separate out what is going on first in the setting of affine reflection groups. This is independent of the application to algebraic grou …
- 503
41
votes
2
answers
2k
views
Implications of non-negativity of coefficients of arbitrary Kazhdan-Lusztig polynomials?
In their seminal 1979 paper Representations of Coxeter groups and Hecke algebras (Invent. Math. 53, doi:10.1007/BF01390031),
Kazhdan and Lusztig studied an arbitrary Coxeter group $(W,S)$ and the corr …
- 35.5k
9
votes
2
answers
687
views
Reference for embeddings of reflection groups (related to folding ADE Coxeter graphs)?
There are a couple of indirect methods, using Lie theory or Springer's general theory of regular elements in (real, complex) reflection groups, to construct natural embeddings among certain Weyl group …
- 63.9k
5
votes
Accepted
Eigenvalues for elements of (infinite) Coxeter groups
The eigenvalues of elements of infinite order are certainly not trivial to study,
and as far as I know little has been determined about them.
Keep in mind that arbitrary infinite Coxeter groups are qu …
- 2,175
4
votes
Reference for embeddings of reflection groups (related to folding ADE Coxeter graphs)?
Rather than overload the question with side remarks, I'll add some background here in community-wiki format to indicate what can be gotten from Springer's relatively elementary treatment of regular el …
- 2,175
2
votes
Coordinates of the Weyl vector of $E_8$ (and the 135 classes of $W(E_8)/W(D_8)$)
Concerning the first question in the header (and some of your preparatory remarks), it's useful to keep in mind the Planche VII for $E_8$ at the end of Chapters 4-6 of Bourbaki's treatise Groupes et a …
- 52.9k
5
votes
Accepted
Recursive formula for inverse Kazhdan-Lusztig polynomials
The case of an affine Weyl group is apparently the only one which has been looked at closely. But it may be hard to answer your specific question. As far as I know, there are two relevant papers, …
- 52.9k
3
votes
Accepted
Reduced decomposition for Weyl group elements which support a Bessel function
I'd be extremely surprised if such tables or database existed, mainly because the number of possible reduced decompositions for a Weyl group element tenda to grow very large as the rank increases. …
- 52.9k
7
votes
1
answer
470
views
Centralizer of longest element in a finite irreducible Weyl group: related to folding of ADE...
Say $(W,S)$ is a finite Coxeter group, such as a Weyl group (which satisfies an additional crystallographic condition). Assume also that $W$ is irreducible. Then it has a longest element $w_o$ r …
- 2,449
2
votes
Bounding weight multiplicities by number of certain Coxeter elements
Though I can't answer the question directly, it may be helpful to clarify some of the issues here. First, it's usually best to focus on the case when $W$ (or the root system of the Lie algebra) is …
- 52.9k
3
votes
Implications of non-negativity of coefficients of arbitrary Kazhdan-Lusztig polynomials?
Maybe I can provide a belated kind of answer to my own question, which I came across when looking for something else in the older literature. Vinay Deodhar published a paper in 1990 here (just before …
- 52.9k
4
votes
Fundamental invariants for root subsystems
[EDIT] Maybe it's useful after all this time to give a more complete and uniform answer to both of the questions asked, by referring to Theorem 3.4(i) in Springer's 1974 paper on regular elements of f …
- 52.9k
24
votes
2
answers
609
views
Uniform proof that a finite (irreducible real) reflection group is determined by its degrees?
Given a finite (irreducible real) group $G$ generated by reflections acting on euclidean $n$-space, it was shown by Chevalley in the 1950s that the algebra of invariants of $G$ in the associated polyn …
- 3,271
2
votes
Are the orders of the generators of a group and the product of pairs of thereof enough for t...
As Geoff points out, the answer is likely to be no, though it takes some work to apply the known finite group theory here. It should be emphasized in the question that the group considered is finite …
- 52.9k
2
votes
On the vertices of a Coxeter complex
There are different viewpoints in the literature about what constitutes an "affine Coxeter group" and its "Coxeter complex", so it would be helpful to specify what source you are following here. Co …
- 52.9k